Barack Obama and Mitt Romney are neck and neck in the race for the White House, but the president's Republican challenger holds a clear advantage in the battle for crucial independent voters, according to a new poll.

A CNN/ORC International survey has found that 49 percent of registered voters say they would vote for Obama if the November election were held today, while 46 percent say they would choose Romney.

Not only is Obama's advantage within the survey's sampling error, the president is also down to a three point margin from the nine point advantage he had in CNN's last national poll conducted in early April.

The poll, conducted from May 29-31 with 1,009 adults nationwide and released Friday, had an overall sampling error of plus or minus three percentage points, with a sampling error of plus or minus 3.5 percentage points for registered voters.

The survey also indicates that Romney holds a 51 percent to 39 percent advantage in the battle for independent voters, even as it found that nearly three-quarters of the voters say they have decided who they will vote for in November, with one in four saying they might change their mind.

The poll showed that 52 percent believe the economy remains issue number one, as compared to the 18 percent who say the deficit is the top issue.

When it comes to who voters think has a better understanding of the economy, "That's a tie as well – 45% pick Obama, 45% choose Romney," said CNN Polling Director Keating Holland, according to CNN.

Further, one in five say neither of the two candidates can fix the economy, with another one in five saying the economy will recover regardless of who wins in November. Among the rest, there is no clear advantage – 31 percent say economic conditions will improve only if Romney wins; 28 percent think things will get better only if Obama stays in office.

"The public splits down the middle on Romney's business experience as well," added Holland. "Fifty percent say that Romney has the right experience to reduce unemployment and improve the economy if he were elected, with 45% saying he does not."

However, there appears to be more enthusiasm among Obama's supporters than that of Romney's, the poll found. More than six in 10 Obama voters say they strongly support the president, while only 47 percent of Romney voters feel that way about their candidate.

Meanwhile, Romney's supporter Donald Trump continued to raise the issue about Obama's birthplace and suggested, apparently taking a dig at the president, that waging war with Iran might be "good politics" for someone seeking re-election.

"There's one line called 'place of birth,'" CNN quoted Trump as saying, speaking of Obama's college records. "I'd like to see what he said," he said during his keynote address at the North Carolina state Republican convention Friday. "It would be very interesting. I don't care what his marks were. I don't care if he had good marks, I'd just like to see 'place of birth.' Perhaps it's going to say Hawaii. Perhaps it's going to say Kenya."

The real estate magnate went on to say that war with Iran over its nuclear program "may be good politics," alluding to Obama, as he added "like somebody wanting to get elected, and the only way he's going to do that is to start a war with Iran."

Romney's campaign has said the candidate accepts where Obama was born, and that they will focus on the economy.